Comments on Change in annihilation delay time

IL NUOVO CIMENTO
VOL. 110 A, N. 4
Aprile 1997
Changes in the annihilation delay time distribution of
stopped antiprotons in helium gas, due to contaminants. - II
THE OBELIX COLLABORATION
A. BERTIN (1), M. BRUSCHI (1), I. D’ANTONE (1), S. DE CASTRO (1), A. FERRETTI (1)
D. GALLI (1), B. GIACOBBE (1), U. MARCONI (1), M. PICCININI (1), N. SEMPRINI CESARI (1)
R. SPIGHI (1), S. VECCHI (1), A. VEZZANI (1), F. VIGOTTI (1), M. VILLA (1), A. VITALE (1)
A. ZOCCOLI (1), M. CORRADINI (2), A. DONZELLA (2), E. LODI RIZZINI (2)
L. VENTURELLI (2), A. ZENONI (3), C. CICALÓ (4), A. MASONI (4), G. PUDDU (4)
S. SERCI (4), P. TEMNIKOV (4), G. USAI (4), V. G. ABLEEV (5), O. YU. DENISOV (5)
O. E. GORCHAKOV (5), S. N. PRAKOV (5), A. M. ROZHDESTVENSKI (5)
M. G. SAPOZHNIKOV (5), V. I. TRETYAK (5), P. GIANOTTI (6), C. GUARALDO (6)
A. LANARO (6), V. LUCHERINI (6), F. NICHITIU (6), C. PETRASCU (6), A. ROSCA (6)
C. CAVION (7), U. GASTALDI (7), M. LOMBARDI (7), A. VORONIN (8), M. MORANDO (9)
R. A. RICCI (10), G. BENDISCIOLI (11), V. FILIPPINI (11), A. FONTANA (11)
P. MONTAGNA (11), A. ROTONDI (11), A. SAINO (11), P. SALVINI (11), M. AGNELLO (12)
F. IAZZI (12), B. MINETTI (12), F. BALESTRA (13), E. BOTTA (13), T. BRESSANI (13)
M. P. BUSSA (13), L. BUSSO (13), D. CALVO (13), P. CERELLO (13), S. COSTA (13)
F. D’ISEP (13), L. FAVA (13), A. FELICIELLO (13), L. FERRERO (13), A. FILIPPI (13)
R. GARFAGNINI (13), A. GRASSO (13), A. MAGGIORA (13), S. MARCELLO (13), D. PANZIERI (13)
D. PARENA (13), E. ROSSETTO (13), F. TOSELLO (13), G. V. MARGAGLIOTTI (14), G. PAULI (14)
C. RIZZO (14), S. TESSARO (14), E. ZAVATTINI (14), L. SANTI (15)
(1) Dipartimento di Fisica, Università di Bologna - Bologna, Italy
INFN, Sezione di Bologna - I-40100 Bologna, Italy
(2) Dipartimento di Elettronica per l’Automazione, Università di Brescia - Brescia, Italy
INFN, Sezione di Torino - Torino, Italy
(3) Dipartimento di Elettronica per l’Automazione, Università di Brescia - Brescia, Italy
INFN, Sezione di Pavia - Pavia, Italy
(4) Dipartimento di Scienze Fisiche, Università di Cagliari - Cagliari, Italy
INFN, Sezione di Cagliari, Cagliari, Italy
(5) Joint Institute for Nuclear Research - Dubna, SU-101000 Moscow, Russia
(6) Laboratori Nazionali di Frascati dell’INFN - I-00044 Frascati, Italy
(7) Laboratori Nazionali di Legnaro dell’INFN - I-35020 Legnaro, Padova, Italy
(8) PN Lebedev Physics Institute - Moscow, Russia
(9) Dipartimento di Fisica, Università di Padova - Padova, Italy
INFN, Sezione di Padova - I-10125 Padova, Italy
(10) Dipartimento di Fisica, Università di Padova - Padova, Italy
INFN, Sezione di Padova - I-10125 Padova, Italy
Laboratori Nazionali di Legnaro dell’INFN - I-35020 Legnaro, Padova, Italy
(11) Dipartimento di Fisica Nucleare e Teorica, Università di Pavia - Pavia, Italy
INFN, Sezione di Pavia - I-27100 Pavia, Italy
(12) Politecnico di Torino - Torino, Italy
INFN, Sezione di Torino - I-10125 Torino, Italy
(13) Dipartimento di Fisica, Università di Torino - Torino, Italy
INFN, Sezione di Torino - I-10125 Torino, Italy
419
A. BERTIN, M. BRUSCHI, I. D’ANTONE, ETC.
420
(14) Dipartimento di Fisica, Università di Trieste - Trieste, Italy
INFN, Sezione di Trieste - I-34127 Trieste, Italy
(15) Dipartimento di Fisica, Università di Udine - Udine, Italy
INFN, Sezione di Trieste - I-34127 Trieste, Italy
(ricevuto l’1 Aprile 1997; approvato il 14 Aprile 1997)
Summary. — A different type of analysis was performed to study the effect of
contaminants on the temporal distribution of delayed annihilations of antiprotons
stopped in helium gas, with respect to some first results published in ABLEEV et. al.
(Nuovo Cimento A, 107 (1994) 1325). A more objective criterion was established to
single out a slow part in the total delayed component, in order to deduce from this,
for each case, the mean value of the product (ys)c , l of the quenching cross-section
and the mean velocity of contaminant molecules, and the fraction of the slow
component h c , l . The fraction h c , l was found to be amazingly stable for each impurity,
independent of the concentration: around 79% of the total delayed component for all
the atomic impurities (Ar , Ne , Xe) and 64% for the molecular ones (H2 , N2 ).
PACS 25.43 – Antiproton-induced reactions.
1. – Introduction
It is now well established [1-5] that by stopping antiprotons in helium one observes
annihilation events, for which the temporal distribution is composed of:
A) A prompt component—corresponding to a fraction e of about 97% of the
stopped antiprotons—contained within a short temporal interval Dt (depending on the
density of the helium target). Here, by short temporal interval one means an interval
of time justifiable with the slowing-down time necessary for the antiproton stopping
plus an interval of time caused by a fast atomic cascade (essentially made up of
processes in which relatively slow radiative decays are negligible). For the case of
antiprotons stopped in a target of helium at 3.0 atm and 20 7C—as in the case we are
considering in this note—Dt is about 50 ns altogether.
B) A delayed component (containing the remaining h 4 1 2 e ` 3 % ), visible of
course after the prompt peak mentioned, with a temporal distribution for which the
average atb is around 3 ms, i.e. events for which before the annihilation, relatively slow
radiative processes are dominant in the cascade.
Surprisingly this behaviour remains about the same for antiprotons stopped in
helium, either at the density of liquid helium, or down to densities corresponding to a
gaseous helium target at 5 mbar (RT) [2, 6]. It should be noted that below these
pressures the slowing-down time for the antiprotons is comparable with or bigger than
the radiative cascade time itself, making the above-mentioned distinction unclear.
Whether the helium antiprotonic systems, from which the delayed component
originates, are atomic, molecular cluster, neutral or charged, and in which states the
antiprotonic complex is initially formed has still not been clarified. It may in fact pass
CHANGES IN THE ANNIHILATION DELAY TIME DISTRIBUTION OF STOPPED ANTIPROTONS ETC.
421
through different systems depending on the target density. However, as first
emphasized in [7] there have to be systems for which Stark effects induced by
neighbouring helium atom collisions are inefficient and Auger transitions are quite
reduced.
In order to gain insight into this problem we experimentally studied the temporal
distributions of delayed annihilations by stopping antiprotons in a pure helium target
(3.0 atm RT) and then looking at changes in the annihilation temporal distributions
caused by adding small quantities of different contaminants to pure helium. The
measurements were carried out with the OBELIX apparatus in August 1992 and the
raw experimental spectra were presented in [8], together with the results of the
analysis.
In [8] we analysed each spectrum—the delayed components—in terms of an
average time atbc (where c identifies the contaminant and its concentration) and the
relation (which should be valid within the limit of very small contaminant
concentrations):
(1)
1
atbc
1
4
atb 4He
11l c
with
(2)
atbc 4
! n (t 2 t )
!n
i
i
0
i
,
i
i
where atb4He is the value for pure helium, t0 is the zero of the temporal scale, and
(3)
– s
–
l c4r c y
c c ,
– is the average relative velocity of the contaminant molecules with respect to
where y
c
the antiproton-helium systems, and the contaminant molecular concentration r c is
defined as:
(4)
r c4
pc
kT
(pc is the partial pressure of the contaminant gas; k is the Boltzmann constant; T is the
absolute temperature).
–
Given these assumptions we defined a kind of average quenching cross-section s
c
of the delayed component, in the antiprotonic system present in the 3 atm helium gas
target, caused by collisions with the atoms of the contaminant.
We observed that the temporal distributions in experimental spectra are not
exhaustively described by the single parameter atbc . In fact, looking at the temporal
distributions of annihilation events close to the prompt peaks, one clearly observes a
region where faster components of delayed annihilations are present [6].
This fact prompts us to look for a different mathematical procedure for handling the
data, in order to get an idea of its impact, particularly on the long time components.
In this paper we wish to present the results of a different type of analysis of the
data published in [8]. In this paper, we have tried to establish a more objective criterion
to single out the slower part in the total fraction e of delayed annihilations, for each
A. BERTIN, M. BRUSCHI, I. D’ANTONE, ETC.
422
TABLE I.
Target
Pressure (mbar)
Contaminant
Partial pressure (mbar)
4
3039
H2
2.5
2.5/3
2.5/9
Xe
5.0
5.0/3
5.0/9
Ar
5.0
5.0/3
5.0/9
Ne
5.0
5.0/3
N2
2.5
—
—
He
Pure 4He
3039
(N.B. 5 mbar corresponds to about 1650 ppm, and 5/9 mbar corresponds to about 180 ppm).
contaminant and its concentration values. As a supplementary result we also obtained
some interesting information about the faster part (later on we name it the residual
part) of delayed annihilations.
In order to do this, for each case we deduce the relative fraction h c , l , to look for
possible regularities, and we also directly infer the values of the product (ys)c , l (from
now on the subscript l indicates the slower part of delayed annihilations).
In table I the different conditions of data acquisition considered in this analysis are
reported.
Before describing the different steps followed in this analysis, we briefly restate
that the nuclear capture time of the antiprotons was measured by detecting the
annihilation charged products by means of plastic scintillation telescopes surrounding
the target (two or more charged particles were requested by the trigger). The
cylindrical target was put in a region were an axial magnetic field (5000 G) was present
in order to focalize the antiproton beam toward the central region of the target [9]. The
zero time was given by the entrance plastic scintillator monitor. The initial antiproton
momentum was 200 MeV/c.
Prompt as well as delayed annihilations were recorded in a temporal interval 40 ms
wide, with a temporal resolution of 19.53 ns per channel.
2. – The method
For each temporal distribution the analysis proceeds through several steps.
A) Data were fitted after 20 ms (we assume that this region is entirely of
accidental origin) with an exponential, in order to find the slope and the fraction of the
accidental events. In the analysis presented in [8], the slope was fixed for all the runs to
CHANGES IN THE ANNIHILATION DELAY TIME DISTRIBUTION OF STOPPED ANTIPROTONS ETC.
423
Fig. 1. – Typical distributions of atbc (ti ) values vs. (ti ). For each distribution we chose, for atbc , l ,
the maximum value assumed by atbc (ti ).
the value obtained in just one dedicated run extremely rich in accidental events.
In the present detailed analysis, the inverse slopes of accidental events of each
temporal spectrum were all found to be at least 100 ms.
The data to be analysed were therefore obtained, for each run, after subtraction of
the estimated accidental events from the experimental spectra.
B) We defined an average time atbc (ti ) in the temporal interval (ti ; 20 ms )
(remember that the zero time value corresponds to the temporal position of the peak of
prompt annihilations) as a function of the time (ti ):
20
(5)
20
!(t 2 t ) n (t ) !(t 2 t ) n (t )
atb (t ) 4
4
N (t )
! n (t )
ti
c
i
k
i
c
20
ti
k
ti
k
i
c
c
c
k
,
i
k
where Nc (ti ) represents the total number of events from ti onwards, nc (tk ) is the
number of events falling in the k-th bin (corresponding to the time tk ) of each spectrum
after subtraction of accidental events, and all times are with respect to the time
position t0 4 0 of the prompt annihilation peak.
A. BERTIN, M. BRUSCHI, I. D’ANTONE, ETC.
424
TABLE II.
Target
atb0 ns
atbl ( ns )
atbres ( ns )
h tot %
h l /h tot
h res /h tot
Pure 4He 3.0 atm 2898 6 133
3038 6 127 1549 6 2300
3.08 6 0.02
0.95 6 0.02
0.05 6 0.02
Contam. Partial
press.
(mbar)
atbc , 0 ( ns )
atbc , l ( ns )
h c , tot %
h c , l / hc , tot
h c , res /h c , tot
Xe
5.0
5.0/3
5.0/9
234 6 4
551 6 18
1114 6 43
271 6 4
658 6 20
1299 6 43
147 6 37
334 6 102
656 6 251
2.85 6 0.02
2.99 6 0.02
3.04 6 0.02
0.81 6 0.02
0.80 6 0.02
0.83 6 0.02
0.19 6 0.02
0.20 6 0.02
0.17 6 0.02
Ar
5.0
5.0/3
5.0/9
1829 6 109
2157 6 122
2418 6 127
2378 6 97 1080 6 297
2781 6 104 1262 6 346
2962 6 110 1394 6 471
2.65 6 0.02
2.90 6 0.02
2.93 6 0.02
0.75 6 0.02
0.76 6 0.02
0.80 6 0.02
0.25 6 0.02
0.24 6 0.02
0.20 6 0.02
Ne
5.0
5.0/3
1358 6 62
2208 6 125
1736 6 61
901 6 201
2490 6 120 1302 6 773
3.03 6 0.02
3.09 6 0.02
0.70 6 0.02
0.86 6 0.02
0.30 6 0.02
0.14 6 0.02
H2
2.5
2.5/3
2.5/9
163 6 9
425 6 15
923 6 30
211 6 9
585 6 17
1220 6 31
115 6 25
290 6 49
608 6 105
2.93 6 0.03
3.00 6 0.02
3.02 6 0.02
0.65 6 0.02
0.63 6 0.02
0.68 6 0.02
0.35 6 0.02
0.37 6 0.02
0.32 6 0.02
N2
2.5
1418 6 85
2212 6 65
922 6 157
2.87 6 0.02
0.60 6 0.02
0.40 6 0.02
atbc , res ( ns )
For each contaminant and its concentration, the calculated value of atbc (ti ) is found
to be constant within 5% over a relatively wide range of values of (ti ): we then chose as
the average time of the slow delayed component, the maximum value of atbc (ti ) in that
temporal range, corresponding to ti* , and we shall call it atbc , l (figs. 1a)-d)).
C) We defined the fraction h c , l for the slow delayed component, as
(6)
h c, l 4
N(ti ) 1 M(ti , atbc , l )
Ntot
,
where M(ti , atbc , l ) is obtained by extrapolating it from ti back to t0 4 0 (the position of
the prompt annihilation peak), by means of an exponential of slope atbc , l normalized to
N(ti ).
Ntot is obviously the total number of all antiproton annihilations experimentally
observed.
D) The delayed annihilations which contribute to the part of temporal spectra
between t0 and ti* (the time from which, for each spectrum, the values of atbc , l reported
in table II are deduced) are called residuals. We calculate the values of
(7)
h c , res
h c , tot
4
u
h c , tot 2 h c , l
h c , tot
v
CHANGES IN THE ANNIHILATION DELAY TIME DISTRIBUTION OF STOPPED ANTIPROTONS ETC.
425
and
(8)
atbc , res 4
a c , res atbc , 0 atbc , l
atbc , l 2 a c , l atbc , 0
as
a c , res 4
h c , res
h c , tot
and
a c, l 4
h c, l
h c , tot
4 ( 1 2 a c , res ) .
It should be noted that, in this case, the proximity of prompt peak contributes
significantly, together with the lower statistical contents, to the growth of errors
associated with the values obtained using (7) and (8).
Owing to our limited temporal resolution (19.53 ns per channel), we could not
explore the zone close to the prompt peak in the range of a few tens of ns. Therefore we
made the arbitrary statement that for each spectrum atbc , 0 4 atb (ti 4 1 4 39 ns )
represents the mean time of the complete distribution of delayed events, and h c , tot 4
[N(t1 ) 1 M(t1 , atbc , 0 ) ] /Ntot represents the corresponding total fraction of delayed
events. This choice implies, in our case, a systematic underestimation of the total
fraction of delayed events, ranging from about 1.1% for pure 4He to about 2.3%, for 4He
plus 2.5 mbar of H2 .
In the following we report our data without taking into account this systematic
underestimation.
3. – Summary of results
In table II the values of the average times atbl , atbres , atbc , l and atbc , res , together with
the relative fractions h l /h tot , h res /h tot , h c , l /h c , tot and h c , res Oh c , tot , are reported, with
the values of atb0 , h tot , atbc , 0 and h c , tot . The errors reported for h res /h tot and h c , res /h c , tot
values are obtained by propagating the errors from eq. (7).
In figs. 2 and 3, for each contaminant, the inverse values of the average times, 1 /atbl ,
1 /atbc , l and 1 /atbres and 1 /atbc , res , are plotted as a function of the partial pressure pc ,
showing, for each contaminant, amazingly good linear behaviour.
Moreover the remarkably large differences (see table II) between the numerical
values of h l /h tot , h res Oh tot and h c , l /h c , tot and h c , res Oh c , tot , suggest that we should look
only at the values of 1 /atbc , l and 1 /atbc , res corresponding to the non-zero concentrations
of contaminants.
The results of linear fits for the values of 1 /atbc , l and 1 /atbc , res , for the non-zero
concentration of Xe, Ar, Ne and H2 , are also shown in figs. 2 and 3.
Extrapolating these fits to the point of zero concentration we found, for the slow
delayed components, values significantly higher than for pure 4He for Xe and H2 ,
whereas Ar and Ne, the less effective contaminants in reducing atbc , l and atbc , res give
values similar to that of pure 4He.
In the case of residue components, for Xe and H2 we found values higher than the
central value of pure 4He but within the errors, whereas Ar and Ne give values
substantially in agreement with the central value of pure 4He.
Because of these results and especially for the very probable dependence of the
– , we decided
formation mechanism of metastable structure on the average velocity y
c
426
A. BERTIN, M. BRUSCHI, I. D’ANTONE, ETC.
Fig. 2. – Values of 1 /atbc , l vs. the partial pressure pc of contaminant gas.
Fig. 3. – Values of 1 /atbc , res vs. the partial pressure pc of contaminant gas.
not to restrict our results to any particular hypothesis about the type and formation
mechanism of the metastable structure itself.
To fit the values of 1 /atbc , l and 1 /atbc , res with their associated errors, we therefore
CHANGES IN THE ANNIHILATION DELAY TIME DISTRIBUTION OF STOPPED ANTIPROTONS ETC.
427
TABLE III.
Contam.
Xe
Ar
Ne
H2
g
Partial
press
(mbar)
rc
5.0
5.0/3
5.0/9
12.07452
4.024839
1.341613
5.0
5.0/3
5.0/9
12.07452
4.024839
1.341613
5.0
12.07452
contam . at .
17
10 cm
5.0/3
4.024839
2.5
2.5/3
2.5/9
24.14904
8.049679
2.683226
3
h u v
v
(ys)c , l
( 10218 cm3 /s )
u
0.81 6 0.02
2.724 6 0.060
0.19 6 0.02 4.97 6 1.63
0.77 6 0.02
0.077 6 0.020
0.23 6 0.02 0.19 6 0.31
0.78 6 0.02
0.217 6 0.034
0.22 6 0.02 0.43 6 0.65
0.65 6 0.02
1.753 6 0.068
0.35 6 0.02 3.28 6 0.16
h c, l
h c , tot
av
h c , res
h c , tot
av
(ys)c , res
( 10218 cm3 /s )
considered the linear relations
(9)
1
atbc , l
4 bc , l 1 r c (ys)c , l
and
(10)
1
atbc , res
4 bc , res 1 r c (ys)c , res ,
where bc , l and bc , res dimensions are [t]21 , and r c dimensions are [contaminant
atoms/cm3 ].
We then obtained the values of (ys)c , l and (ys)c , res reported in table III.
To significantly reduce the rather high errors on atbc , res—and consequently on
(ys)c , res—reported in table III, it is necessary to reduce the errors on atbc , 0 and atbc , l,
and this can be obtained only with much greater statistical content of temporal
spectra.
4. – Conclusions
–
Our data and results concern p impinging on a 4He target at 3.0 atm (RT), in which
we introduce very small quantities of atomic (Ar, Ne, Xe) and molecular (H2 , N2 )
contaminants.
From the behaviour of our results we can deduce that contaminants do not interfere
with the primary stage of the formation mechanism of metastable structures. The
absolute value of the total fraction of delayed events h c , tot is in fact amazingly constant
and close to 3.08% the value for pure 4He, for each contaminant and concentration.
On the contrary, looking at the values of h c , l /h c , tot and h c , res /h c , tot , we can confirm
428
A. BERTIN, M. BRUSCHI, I. D’ANTONE, ETC.
that contaminants contribute to define the relative populations of the two different
metastable groups: the long living and the shorter living (residuals). In particular,
molecular contaminants ( H2 , N2 ) populate the shorter-living group more than
monoatomic contaminants (Ar, Ne,Xr). If we look now at the values of the fraction h c , l
for each selected long-living component, we see, except for Ne, an amazing stability
independent of the impurity and its concentration (see h c , l /h c , tot in table II and
(h c , l /h c , tot ) in table III): for the monoatomic impurities (Ar, Xe), h c , l is about the same
for all of them, around 79% of the total delayed component; for the molecular
impurities (H2 , N2 ), h c , l is about 64% of the total delayed component, but in any case it
is significantly lower than 95%, the value of pure 4He.
This suggests to us that contaminants do not mix long-living and shorter-living
groups, but only contribute to their initial formation.
For the long-living components we also see that the linear behaviour of the
disappearance rate 1 /atbc , l as a function of the impurity concentrations (fig. 2) is clearly
shown for a wide range of impurity concentrations, at least for Xe and H2 . Moreover
the behaviours for Ne and Ar are clearly shown, indicating that Ne is a more effective
quenching element than Ar. We also observed similar behaviour for the residuals
(fig. 3), and the values so obtained for (ys)c , l and (ys)c , res are reported in table III.
Looking now at the unsuccessful correspondence between the extrapolation at zero
concentration of fits for 1 /atbc , l values, for Xe and H2 we can suppose a saturation effect
fulfilled before the linear behaviour evidenced out by our experimental values, that is
for very small values of contaminant concentrations (lower than 180 ppm of contaminant molecules).
–
Remembering the low rate of the p beam (between 10 and 20 kHz), we see that each
–
p impinging on the target falls to a prompt or delayed annihilation almost before the
–
following p enters the target.
With this statement, our results indicate, in the explored range of contaminant
pressure, a direct dependence of the quenching effect on the absolute number of
contaminant molecules.
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[1]
[2]
[3]
[4]
[5]
[6]
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IWASAKI M. et al., Phys. Rev. Lett., 67 (1991) 1246.
WIDMANN E. et al., Phys. Rev. A, 53 (1996) 3129.
YAMAZAKI T. et al., Nature, 361 (1993) 238.
MARGAGLIOTTI G. V., On time distribution of late annihilations following stopping
antiprotons in 4He gas contaminated with impurities, in 6th Workshop on Exotic
Atoms, Molecules and their Interactions, Erice 21-30 March 1994, INFN/AE-94/24, p. 173.
[7] CONDO G. T., Phys. Lett., 9 (1964) 65.
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[9] ADAMO A. et al., Yad. Fiz., 55 (1992) 3009, where a detailed description of the OBELIX
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